Power flow calculations are an essential stage in many planning and control applications for distribution systems.To use these in control applications, however, the calculation time needs to be improved, and this can be done by the use of a trained ANN. This paper presents the considerations for constructing ANNs for DSs, and describes a method for training the system in order to support switching events representing a change in topology. The solutions for three DSs, balanced as well as unbalanced, are presented and the various considerations affecting the most appropriate ANN construction are discussed. The results are compared to the solution from the classical complex Newton-Raphson and the fixed-point iterative methods. The solutions have very high precision and good results are found for switched laterals. The computational performance is also compared and an improvement of two orders of magnitude is observed.